Construction of KMS States in Perturbative QFT and Renormalized Hamiltonian Dynamics

Abstract

We present a general construction of KMS states in the framework of perturbative algebraic quantum field theory (pAQFT). Our approach may be understood as an extension of the Schwinger-Keldysh formalism. We obtain in particular the Wightman functions at positive temperature, thus solving a problem posed some time ago by Steinmann. The notorious infrared divergences observed in a diagrammatic expansion are shown to be absent due to a consequent exploitation of the locality properties of pAQFT. To this avail, we introduce a novel, Hamiltonian description of the interacting dynamics and find, in particular, a precise relation between relativistic QFT and rigorous quantum statistical mechanics.

43 pages, 4 figures

References in corpus (5)

• The time slice axiom in perturbative quantum field theory on globally hyperbolic spacetimes
• Dimensional Regularization in Position Space and a Forest Formula for Regularized Epstein-Glaser Renormalization
• Unruh Effect and the Concept of Temperature
• The relativistic KMS condition for the thermal n-point functions of the P(ϕ)_2 model
• Thermal Quantum Fields with Spatially Cut-off Interactions in 1+1 Space-time Dimensions

Cited by in corpus (16)

• A C*-algebraic approach to interacting quantum field theories
• The generalised principle of perturbative agreement and the thermal mass
• Weak adiabatic limit in quantum field theories with massless particles
• The universal C*-algebra of the electromagnetic field
• Constructing Hadamard states via an extended Møller operator
• Linear stability of semiclassical theories of gravity
• On the stability of KMS states in perturbative algebraic quantum field theories
• Relative entropy and entropy production for equilibrium states in pAQFT
• Configuration Space BPHZ Renormalization on Analytic Spacetimes
• Equilibrium states in Thermal Field Theory and in Algebraic Quantum Field Theory
• Massless fields and adiabatic limit in quantum field theory
• Perturbative Algebraic Quantum Field Theory on Quantum Spacetime: Adiabatic and Ultraviolet Convergence
• Classical KMS Functionals and Phase Transitions in Poisson Geometry
• Quantum Spacetime and the Universe at the Big Bang, vanishing interactions and fading degrees of freedom
• Secular growths and their relation to equilibrium states in perturbative QFT
• Thermal state with quadratic interaction